Tithi

Retrieved from "http://en.wikipedia.org/wiki/Tithi"

Interview with Dr. Subhash Kak

Atithi The etymology of Samskrta  phrases never ceases to amaze. For example take the case of Atithi which means Guest in  S.  But atithi also means the antonym of Tithi which denotes a specific time.  Atithi can therefore be interpreted as the person who may arrive at any random time ,and should by implication be welcomed whenever he/she arrives. Imagine, all that meaning packed in one word simply by prefixing a अ

Moore links  and miscellaneous notes can be found here including the back calculation of the Tithi pertaining to a  past date.

http://csep10.phys.utk.edu/astr161/lect/index.html

Some Definitions to get started
ecliptic  क्तांतीव्रुत्त (Kranthivruth)

(ēklĬp´tĬk, Ĭ-) , the great circle on the celestial sphere that lies in the plane of the earth's orbit (called the plane of the ecliptic). Because of the earth's yearly revolution around the sun, the sun appears to move in an annual journey through the heavens with the ecliptic as its path. The ecliptic is the principal axis in the ecliptic coordinate system . The two points at which the ecliptic crosses the celestial equator are the equinoxes . The obliquity of the ecliptic is the inclination of the plane of the ecliptic to the plane of the celestial equator, an angle of about 23 1/2 °. The constellations through which the ecliptic passes are the constellations of the zodiac .

equinox

वसंत संपत (Vasanth Sampat) Vernal equinox

(ē´kwĬnŏks) , either of two points on the celestial sphere where the ecliptic and the celestial equator intersect. The vernal equinox, also known as “the first point of Aries,” is the point at which the sun appears to cross the celestial equator from south to north. This occurs about Mar. 21, marking the beginning of spring in the Northern Hemisphere. At the autumnal equinox, about Sept. 23, the sun again appears to cross the celestial equator, this time from north to south; this marks the beginning of autumn in the Northern Hemisphere. On the date of either equinox, night and day are of equal length (12 hr each) in all parts of the world; the word equinox is often used to refer to either of these dates. The equinoxes are not fixed points on the celestial sphere but move westward along the ecliptic, passing through all the constellations of the zodiac in 26,000 years. This motion is called the precession of the equinoxes . The vernal equinox is a reference point in the equatorial coordinate system .

equatorial coordinate system

the most commonly used astronomical coordinate system for indicating the positions of stars or other celestial objects on the celestial sphere . The celestial sphere is an imaginary sphere with the observer at its center. It represents the entire sky; all celestial objects other than the earth are imagined as being located on its inside surface. If the earth's axis is extended, the points where it intersects the celestial sphere are called the celestial poles; the north celestial pole is directly above the earth's North Pole, and the south celestial pole directly above the earth's South Pole. The great circle on the celestial sphere halfway between the celestial poles is called the celestial equator; it can be thought of as the earth's equator projected onto the celestial sphere. It divides the celestial sphere into the northern and southern skies. An important reference point on the celestial equator is the vernal equinox , the point at which the sun crosses the celestial equator in March. To designate the position of a star, the astronomer considers an imaginary great circle passing through the celestial poles and through the star in question. This is the star's hour circle , analogous to a meridian of longitude on earth. The astronomer then measures the angle between the vernal equinox and the point where the hour circle intersects the celestial equator. This angle is called the star's right ascension and is measured in hours, minutes, and seconds rather than in the more familiar degrees, minutes, and seconds. (There are 360 degrees or 24 hours in a full circle.) The right ascension is always measured eastward from the vernal equinox. Next the observer measures along the star's hour circle the angle between the celestial equator and the position of the star. This angle is called the declination of the star and is measured in degrees, minutes, and seconds north or south of the celestial equator, analogous to latitude on the earth. Right ascension and declination together determine the location of a star on the celestial sphere. The right ascensions and declinations of many stars are listed in various reference tables published for astronomers and navigators. Because a star's position may change slightly (see proper motion and precession of the equinoxes ), such tables must be revised at regular intervals. By definition, the vernal equinox is located at right ascension 0 h and declination 0°.

Another useful reference point is the sigma point, the point where the observer's celestial meridian intersects the celestial equator. The right ascension of the sigma point is equal to the observer's local sidereal time . The angular distance from the sigma point to a star's hour circle is called its hour angle ; it is equal to the star's right ascension minus the local sidereal time. Because the vernal equinox is not always visible in the night sky (especially in the spring), whereas the sigma point is always visible, the hour angle is used in actually locating a body in the sky.

2. Astronomical data and the Aryan question

(from Koenrad Elst Book )

2.3. THE PRECESSION OF THE EQUINOX

2.3.1. The slowest hand on the clock


The truly strong evidence for a high chronology of the Vedas is the Vedic information about the position of the equinox.  The phenomenon of the “precession of the equinoxes” takes the ecliptical constellations (also known as the sidereal Zodiac, i.e. those constellations through which the sun passes)12 slowly past the vernal equinox point, i.e. the intersection of ecliptic and equator, rising due East on the horizon.  The whole tour is made in about 25,791 years, the longest cycle manageable for naked-eye observers.  If data about the precession are properly recorded, they provide the best and often the only clue to an absolute chronology for ancient events.

If we can read the Vedic and post-Vedic indications properly, they mention constellations on the equinox points which were there from 4,000 BC for the Rg-Veda (Orion, as already pointed out by B.G. Tilak)13 through around 3100 BC for the Atharva-Veda and the core Mahabharata (Aldebaran) down to 2,300 BC for the Sutras and the Shatapatha Brahmana (Pleiades).14


Other references to the constellational position of the solstices or of solar and lunar positions at the beginning of the monsoon confirm this chronology.  Thus, the Kaushitaki Brahmana puts the winter solstice at the new moon of the sidereal month of Magha (i.e. the Mahashivaratri festival), which now falls 70 days later: this points to a date in the first half of the 3rd millennium BC.  The same processional movement of the twelve months of the Hindu calendar (which are tied to the constellations) vis-a-vis the meterological seasons, is what allowed Hermann Jacobi to fix the date of the Rg-Veda to the 5th-4th millennium BC.15 Indeed, the regular references to the full moon’s position in a constellation at the time of the beginning of the monsoon, which nearly coincides with the summer solstice, provide a secure and unambiguous chronology through the millennial Vedic literature.


It is not only the Vedic age which is moved a number of centuries deeper into the past, when comparing the astronomical indications with the conventional chronology.  Even the Gupta age (and implicitly the earlier ages of the Buddha, the Mauryas etc.) could be affected.  Indeed, the famous playwright and poet Kalidasa, supposed to have worked at the Gupta court in about 400 AD, wrote that the monsoon rains started at the start of the sidereal month of Ashadha; this timing of the monsoon was accurate in the last centuries BC.16 This implicit astronomy-based chronology of Kalidasa, about 5 centuries higher than the conventional one, tallies well with the traditional “high” chronology of the Buddha, whom Chinese Buddhist tradition dates to ca. 1100 BC, and the implicit Puranic chronology even to ca. 1700 BC.17

2.3.2. Some difficulties


These indications about the processional phases may be unreliable insofar as their exact meaning is not unambiguous.  To say that a constellation “never swerves from the East” (as is said of the Pleiades in the Shatapatha Brahmana 2:1:2:3) seems to mean that it contains the spring equinox, implying that it is on the equator, which intersects the horizon due East.  But this might seem insufficiently explicit for the modem reader who is used to a precise and separate technical terminology for such matters.  But then, the modem reader will have to accept that technical terminology in Vedic days mostly consisted in fixed metaphorical uses of common terms.  This is not all that primitive, for the same thing will be found when the etymology of modern technical terms is analyzed, e.g. a telescope is a Greek “far-seer”, oxygen is “acid-producer”, a cylinder is a “roller”.  The only difference is that we can use the vocabulary of foreign classical languages to borrow from, while Sanskrit was its own classical reservoir of specialized terminology.


Another factor of uncertainty is that the equinox moves very slowly (1 degree in nearly 71 years), so that any inexactness in the Vedic indications and any ambiguity in the constellations’ boundaries makes a difference of centuries.  This occasional inexactness might possibly be enough to neutralize the above shift in Kalidasa’s date - but not to account for a shift of millennia (each millennium corresponding to about 14 degrees of arc) needed to move the Vedic age from the pre-Harappan to the post-Harappan period, from 4000 BC as calculated by the astronomers to 1200 BC as surmised by Friedrich Max Müller.


On the other hand, it is encouraging to note that the astronomical evidence is entirely free of contradictions.  There would be a real problem if the astronomical indications had put the Upanishads earlier than the Rg-Veda, or Kalidasa earlier than the Brahmanas, but that is not the case: the astronomical evidence is consistent. Inconsistency would prove the predictable objection of AIT defenders that these astronomical references are but poetical tabulation without any scientific contents.  However, the facts are just the opposite.  To the extent that there are astronomical indications in the Vedas, these form a consistent set of data detailing an absolute chronology for Vedic literature in full agreement with the known relative chronology of the different texts of this literature.  This way, they completely contradict the hypothesis that the Vedas were composed after an invasion in about 1500 BC.  Not one of the dozens of astronomical data in Vedic literature confirms the AIT chronology.

2.3.3. Regulus at summer solstice


In the Shulba Sutra appended to Baudhayana’s Shrauta Sutra, mathematical instructions are given for the construction of Vedic altars.  One of its remarkable contributions is the theorem usually ascribed to Pythagoras, first for the special case of a square (the form in which it was discovered), then for the general case of the rectangle: “The diagonal of the rectangle produces the combined surface which the length and the breadth produce separately.” This and other instances of advanced mathematics presented by Baudhayana have been shown by the American mathematician A. Seidenberg to be the origin of similar mathematical techniques and ‘discoveries’ in Greece and Babylonia, some of which have been securely dated to 1700 BC. So, 1700 BC was a terminus post quem for Baudhayana’s mathematics, which would reasonably be dated to the later part of the Harappan period which ended in ca. 1900 BC.

However, Seidenberg was told by the indologists that these Sutras, or any Vedic text for that matter, were definitely written later than 1700 BC.  But mathematical data cannot be manipulated just like that, and Seidenberg remained convinced of his case: “Whatever the difficulty there may be [concerning chronology], it is small in comparison with the difficulty of deriving the Vedic ritual application of the theorem from Babylonia. (The reverse derivation is easy)… the application involves geometric algebra, and there is no evidence of geometric algebra from Babylonia.  And the geometry of Babylonia is already secondary whereas in India it is primary.”18 To satisfy the indologists, he said that the Shulba Sutra had conserved an older tradition, and that it is from this one that the Babylonians had learned their mathematics: “Hence we do not hesitate to place the Vedic (…) rituals, or more exactly, rituals exactly like them, far back of 1700 BC. (…) elements of geometry found in Egypt and Babylonia stem from a ritual system of the kind described in the Sulvasutras.”19


This is then one of those “entities multiplied beyond necessity”: a ritual, annex altar, annex mathematical theory, which is exactly like the Vedic ritual, annex altar, annex mathematical theory, only it is not the Vedic ritual but a thousand or so years older.  Let us simplify matters and assume that it was Baudhayana himself who devised his mathematical theories “far back of 1700 BC”.  Is there a way to find independent confirmation of this suspicion?  Yes, there is: the precession of the equinoxes.


In their Vedic Index of Names and Subjects, A.A. MacDonell and A.B. Keith cite the opinion of several philologists about a reference to a solstice in Magha in the Baudhayana Shrauta Sutra (as well as in the Kaushitaki Brahmana 19:3), to which the Shulba Sutra is an appendix.  Magha is the asterism around the star Regulus, but the name is used for an entire month (names of months are typically the name of the most prominent one of the two or three asterisms/nakshatras which make up that one-twelfth of the ecliptic), spatially equivalent to a zone of about 300 around that star, so any deduction here must take a fair degree of imprecision into account.  The 18th- and 19th-century philologists cited disagree about whether a Magha solstice was in 1181 BC or in 1391 BC.  The authors themselves consider it “only fair to allow a thousand years for possible errors”, and settle for a date between 800 BC and 600 BC, “quite in harmony with the probable date of the Brahmana literature”.20


However, it is very easy to calculate that Regulus, currently at almost exactly 600 from the solstitial axis, was on that axis about 60 x 71 years ago, i.e. in the 23rd century BC, Though we must indeed allow for an inexactitude of up to 150, equivalent to about 1100 years, the Magha solstice described is much more likely to have been in 2200 BC than in 1100 BC, and Keith and MacDonell’s 600 BC is quite beyond the pale.  It may have taken place even before the 23rd century BC: maybe only the asterism around Regulus had reached the solstitial axis but not yet the star itself.  Most likely, then, this reference to a Magha solstice confirms that the Bra and Sutra literature including the Baudhayana Shrauta Sutra (annex Shulba) dates to the late 3rd millennium BC, at the height of the Harappan civilization.  In that case, Seidenberg’s reconstruction of the development and transmission of mathematical knowledge and the astronomical references in the literature confirm each other in placing Baudhayana’s (post-Vedic!) work in the later part of the Harappan period.

2.3.4. One Veda can hide another


At this point, the only defence for the AIT can consist in a wholesale rejection of the astronomical evidence.  This can be done in a crude way, e.g. by simply ignoring the astronomical evidence, as is done in most explicitations of the AIT.  A slightly subtler approach is to explain it away, as is done by Romila Thapar, who affirms her belief in “the generally accepted chronology that the Rig-Vedic hymns were composed over a period extending from about 1500 to 1000 BC”.  When “references to what have been interpreted as configurations of stars have been used to suggest dates of about 4000 BC for these hymns”, she raises the objection that “planetary positions could have been observed in earlier times and such observations been handed down as part of an oral tradition”, so that they “do not constitute proof of the chronology of the Vedic hymns”.21


This would imply that accurate astronomical data were indeed made from the 5th millennium onwards, and that they were preserved for more than two thousand years, an unparalleled feat in oral traditions.  If such a feat is not an indication of literacy and of written records, at the least it supposes a mnemotechnical device capable of preserving information orally, and the one that was available then was verse.  So, some poems with the memory-aiding devices of verse, rhythm and tone must have been composed when the information was available first-hand, i.e. close to the time of the actual observation, and those hymns would of course be the Vedic hymns themselves.  Otherwise, one has to postulate that the Vedic hymns were composed by borrowing the contents of an earlier tradition of verse, composed at the time when the equinox was observed to be in Orion.


In other words, the Rg-Veda contains literal (though unacknowledged) quotations from another hymns collection composed 2,500 years earlier.  This is as good as asserting that Shakespeare’s works were not written by Shakespeare, but by someone else whose name was also Shakespeare. However, the point to remember is that even Romila Thapar does not deny that somebody’s actual observation of these celestial phenomena was the source of their description in the Vedas.


It is not good enough for those who don’t like this evidence, to object that they are not convinced by these astronomical indications of high antiquity, on the plea that their meaning might be somewhat unclear to us. it is clear enough and undeniable that the Vedic seers took care to mention certain astronomical positions and phenomena.  A convincing refutation would therefore require an alternative but consistent (philogically as well as astronomically sound) interpretation of the existing astronomical indications which brings Vedic literature down to a much later age.  But so far, such a reading of those text passages doesn’t seem to exist.  In no case is there astronomical information which puts the Vedas at as late a date as “generally accepted” by Prof. Thapar and others.
 

Footnotes: 
 

12The sidereal Zodiac, used in astrology by most Hindu and some Western astrologers, consists of the actually visible constellations on the ecliptic.  It is contrasted with the tropical Zodiac, an abstract division of the ecliptic in twelve equal sectors of which the first one starts by definition at the equinox axis.  This tropical Zodiac, used by most Western and some Hindu astrologers, is unrelated to the background of constellations (it could be constructed even if the universe consisted only of the sun and the earth); but it does not figure anywhere in the present discussion.  As far as we know, the process of abstraction from visible constellations to geometrical sectors took place only in the Hellenistic period, ca. 100 BC, and was unknown to the Vedic seers, though they did know the solstice axis and equinox axis.


13We are aware that the equinox axis never points exactly towards the constellation Orion, which lies south of the ecliptic; but it is understand a that the relatively starless area between the constellations of Gemini and Taurus was named after the conspicuous constellation Orion which lies nearby on the same longitude.


14Remark that the second half of the 3rd millennium BC, the high tide of the Harappan cities, is also identified by K.D. Sethna (KarpAsa in Prehistoric India: a Chronological and Cultural Clue, Impex India, Delhi 1981) as the period of the Sutras, the Vedas being assigned to the pre-Harappan period, all on the basis of the evidence of material culture (with special focus on cotton/karpAsa) as attested in the literary and archaeological records. According to Asko Parpola, Indus~Saraswati seal 430 (reasonably datable to the 24th century BC) depicting the Seven Sisters seems to refer to the observation of the Pleiades.